In exercise 2.13, you considered the food stamp programs in the US. Under this program, poor households receive a certain quantity of “food stamps” — stamps that contain a dollar value which is accepted like cash for food purchases at grocery stores.
A. Consider a household with monthly income of $1,500 and suppose that this household qualifies for food stamps in the amount of $500.
(a) Illustrate this household’s budget, both with and without the food stamp program, with “dollars spent on food” (on the horizontal axis) and “dollars spent on other goods” on the vertical. What has to be true for the household to be just as well off under this food stamp program as it would be if the government simply gave $500 in cash to the household (instead of food stamps)?
(b) Consider the following alternate policy: Instead of food stamps, the government tells this household that it will reimburse 50% of the household’s food bills. On a separate graph, illustrate the household’s budget (in the absence of food stamps) with and without this alternate program.
(c) Choose an optimal bundle A on the alternate program budget line and determine how much the government is paying to this household (as a vertical distance in your graph). Call this amount S.
(d) Now suppose the government decided to abolish the program and instead gives the same amount S in food stamps. How does this change the household’s budget?
(e) Will this household be happy about the change from the first alternate program to the food stamp program?
(f) If some politicians want to increase food consumption by the poor and others just want to make the poor happier, will they differ on what policy is best?
(g) True or False: The less substitutable food is for other goods, the greater the difference in food consumption between equally funded cash and food subsidy programs.
(h) Consider a third possible alternative—giving cash instead of food stamps. True or False: As the food stamp program becomes more generous, the household will at some point prefer a pure cash transfer over an equally costly food stamp program.
B. Suppose this household’s tastes for spending on food (x1) and spending on other goods (x2) can be characterized by the utility function u(x1,x2)= αlnx1 +lnx2.
(a) Calculate the level of food and other good purchases as a function of I and the price of food p1 (leaving the price of dollars on other goods as just 1).
(b) For the household described in part A, what is the range of α that makes the $500 food stamp program equivalent to a cash gift of $500?
(c) Suppose for the remainder of the problem that α = 0.5. How much food will this household buy under the alternate policy described in A(b)?
(d) How much does this alternate policy cost the government for this household? Call this amount S.
(e) How much food will the household buy if the government gives S as a cash payment and abolishes the alternate food subsidy program?
(f) Determine which policy — the price subsidy that leads to an amount S being given to the household, or the equally costly cash payment in part (e)—is preferred by the household.
(g) Now suppose the government considered subsidizing food more heavily. Calculate the utility that the household will receive from three equally funded policies: a 75% food price subsidy (i.e. a subsidy where the government pays 75% of food bills), a food stamp program and a cash gift program.